Question

If |a⃗|=|⃗b|=|⃗a+⃗b| , then find the angle between the vectors ⃗a and ⃗b​

Answer 1

Answer:

60°

Step-by-step explanation:

Since,

|a| = |b| = |a + b|

Then , these vectors will form an equilateral triangle.

So,

the angle between the vectors a and b = 60°

Answer 2

Answer:

The angle between vectors a and b is 120°

Step-by-step explanation:

Given that,

|a⃗|=|⃗b|=|⃗a+⃗b|

Let us assume that,

|a⃗|=|⃗b|=|⃗a+⃗b|=k

And the angle between vectors a and b be θ

We know that For Two vectors magnitude of resultant is given by

$k = \sqrt{a {}^{2} + b {}^{2} + 2abcos θ}$

Therefore According to given question,

$k = \sqrt{k {}^{2} + k {}^{2} + 2(k)(k) \cos(θ ) } \\ k = \sqrt{2k {}^{2} + 2k {}^{2} \cosθ }$

Squaring on both sides, we get

$k {}^{2} = 2k {}^{2} (1 + \cosθ) \\ = = > \cosθ = \frac{1}{2} - 1 = \frac{ - 1}{2 } \\ = = > θ = 120 {}^{0}$

Therefore if for a given two vectors a and b,

if |a⃗|=|⃗b|=|⃗a+⃗b| then angle θ=120°

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